Pixellated circle

For applications in optical systems it is often necessary to represent a circular aperture in a pixellated form. An objective parameter is introduced that is a measure of how well an approximate circle can be generated from a small array of square pixels. Both filled circles (disks) and rings are considered. Arrays with a width given by an even number of pixels can also be used to generate quadrants of a circle. Rings with outer and inner profiles given by optimum circles or quadrants can be summed to fill a complete circle or quadrant.